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Proof Search in Nested Sequent Calculi

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9450)

Abstract

We propose a notion of focusing for nested sequent calculi for modal logics which brings down the complexity of proof search to that of the corresponding sequent calculi. The resulting systems are amenable to specifications in linear logic. Examples include modal logic \(\mathsf {K}\), a simply dependent bimodal logic and the standard non-normal modal logics. As byproduct we obtain the first nested sequent calculi for the considered non-normal modal logics.

Keywords

  • Modal Logic
  • Inference Rule
  • Modal Rule
  • Linear Logic
  • Sequent Calculus

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

B. Lellmann—Funded by the EU under Marie Skłodowska-Curie grant agreement No. 660047.

E. Pimentel—Funded by CNPq.

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Correspondence to Björn Lellmann .

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Lellmann, B., Pimentel, E. (2015). Proof Search in Nested Sequent Calculi. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2015. Lecture Notes in Computer Science(), vol 9450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48899-7_39

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  • DOI: https://doi.org/10.1007/978-3-662-48899-7_39

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